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Successful couplings for a class of stochastic differential equations driven by Lévy processes

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Abstract

By constructing proper coupling operators for the integro-differential type Markov generator, we establish the existence of a successful coupling for a class of stochastic differential equations driven by Lévy processes. Our result implies a new Liouville theorem for space-time bounded harmonic functions with respect to the underlying Markov semigroups, and it is sharp for Ornstein-Uhlenbeck processes driven by α-stable Lévy processes.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007, China

    HuoNan Lin & Jian Wang

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  1. HuoNan Lin
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  2. Jian Wang
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Correspondence to HuoNan Lin.

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Lin, H., Wang, J. Successful couplings for a class of stochastic differential equations driven by Lévy processes. Sci. China Math. 55, 1735–1748 (2012). https://doi.org/10.1007/s11425-012-4387-x

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  • DOI: https://doi.org/10.1007/s11425-012-4387-x

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